Kuznetsova Olga M, Johnson Victoria Plamadeala
Late Development Statistics, Merck & Co., Inc., Rahway, New Jersey, U.S.A.
Early Development Statistics, Merck & Co., Inc., Kenilworth, New Jersey, U.S.A.
Stat Med. 2017 Jul 20;36(16):2483-2498. doi: 10.1002/sim.7290. Epub 2017 Mar 23.
The paper discusses three methods for expanding the biased coin randomization (BCR) to unequal allocation while preserving the unconditional allocation ratio at every step. The first method originally proposed in the contexts of BCR and minimization is based on mapping from an equal allocation multi-arm BCR. Despite the improvement proposed in this paper to ensure tighter adherence to the targeted unequal allocation, this method still distributes the probability mass at least as wide as the permuted block randomization (PBR). This works for smaller block sizes, but for larger block sizes, a tighter control of the imbalance in the treatment assignments is desired. The second method, which has two versions, allows to tighten the distribution of the imbalance compared with that achieved with the PBR. However, the distribution of the imbalance remains considerably wider than that of the brick tunnel randomization - the unequal allocation procedure with the tightest possible imbalance distribution among all allocation ratio preserving procedures with the same allocation ratio. Finally, the third method, the BCR with a preset proportion of maximal forcing, mimics the properties of the equal allocation BCR. With maximum forcing, it approaches the brick tunnel randomization, similar to how 1:1 BCR approaches 1:1 PBR with the permuted block size of 2 (the equal allocation procedure with the lowest possible imbalance) when the bias approaches 1. With minimum forcing, the BCR with a preset proportion of maximal forcing approaches complete randomization (similar to 1:1 BCR). Copyright © 2017 John Wiley & Sons, Ltd.
本文讨论了三种将有偏硬币随机化（BCR）扩展到不等分配的方法，同时在每一步都保持无条件分配比例。第一种方法最初是在BCR和最小化的背景下提出的，基于从等分配多臂BCR的映射。尽管本文提出了改进措施以确保更严格地遵循目标不等分配，但该方法仍然至少像置换区组随机化（PBR）一样广泛地分布概率质量。这对于较小的区组大小有效，但对于较大的区组大小，需要对治疗分配中的不平衡进行更严格的控制。第二种方法有两个版本，与PBR相比，它可以收紧不平衡的分布。然而，不平衡的分布仍然比砖隧道随机化宽得多——砖隧道随机化是在所有具有相同分配比例的保持分配比例的程序中不平衡分布尽可能紧的不等分配程序。最后，第三种方法，即具有预设最大强制比例的BCR，模仿等分配BCR的性质。在最大强制下，它接近砖隧道随机化，类似于当偏差接近1时，1:1的BCR在置换区组大小为2（不平衡尽可能低的等分配程序）时接近1:1的PBR。在最小强制下，具有预设最大强制比例的BCR接近完全随机化（类似于1:1的BCR）。版权所有© 2017约翰威立父子有限公司。
